Demand exists for a means of precisely estimating original information using information degraded by transfer. In this case, estimation by means of a transfer function for a transfer system is generally used. If the transfer function of the transfer system is known, and the transfer function takes non-zero value for an entire frequency domain of the original information, it is possible to completely restore the original information from the information obtained after the transfer by means of an inverse filter of the transfer function.
Restoration by means of the above method cannot be directly applied to a case where the transfer function takes a value of zero in certain frequency domain. This is because the inverse filter cannot be defined in the frequency domain where the transfer function takes a value of zero. Thus, the information in the frequency domain where the transfer function takes a value of zero is lost in the course of the transfer in this transfer system. In other words, when information is transferred, the information is not transferred as the exact original; instead it is degraded in the course of the transfer. If an image is transferred in an optical system, for example, the image is degraded resulting in the loss of fine and detailed portions, namely portions with high spatial frequencies, due to aberrations and errors in the devices, and the image is recognized in the degraded state.
There have been technologies proposed to restore degraded information due to losses in specific frequency domain in the course of transfer based on the transfer characteristics of a transfer system and the information after degradation. The technologies for restoring degraded information have been proposed mainly in the field of image processing. Regarding the technology for restoring a degraded image, there is a known method that employs the Richardson-Lucy algorithm, described in W. H. Richardson, “Bayesian-based iterative method of image restoration”, Journal of Optical Society of America, United States, 1972, volume 62, pp 55-59, and L. B. Lucy, “An iterative technique for the rectification of observed distributions”, Astronomical Journal, United States, 1974, volume 79, pp 745-754.
The method employing the Richardson-Lucy algorithm recognizes the formation of light in an image as one event, and restores the original image by means of a method used in a technical field of probability and statistics. The method employing the Richardson-Lucy algorithm normalizes a distribution of illuminance for an original image to recognize the distribution as the distribution of a probability density function for an event of image formation of light on the original image. Moreover, the method normalizes a distribution of illuminance for a degraded image to recognize the distribution as the distribution of a probability density function for an event of image formation of light on the degraded image. A point spread function (PSF), which is a transfer characteristic of an optical system, can be recognized as the distribution of a probability density function of a conditional probability, which represents the distribution of the probability that light forms an image on the degraded image based upon the condition that a point of light forms an image on the original image. The method employing the Richardson-Lucy algorithm estimates, using an iterative calculation, the most probable distribution of distributions for the original image that will realize the distribution of the degraded image based on the distribution of the degraded image and the distribution of the PSF according to the Bayes' theorem. The distribution of the PSF may be calculated from the parameters of the optical system or may be calculated by experimentally acquiring a distribution of an image by actually transferring a point image.
Though the method employing the Richardson-Lucy algorithm is a method to restore a degraded image, the same method may be used to restore original information from degraded information for other types of information such as the history of an electric potential.